This is a tricky area. Technically, since there is presumably valid paperwork pertaining to the issue, the hospital should follow the directive.
However, if the treatment team truly believes that continued life support will not accomplish anything other than keeping the bills building up they do have the right to take the proxy to court, request that the patient becomes either a ward of the State, treating physician or something along those lines, and then make the decision themselves.
Going against the wishes of the proxy without getting done legally can lead to an awful lot of trouble.